A grinding machine of the type to which the invention relates is for example known from U.S. Pat. No. 6,190,242. With this known grinding machine, the workpiece carrier supporting the workpiece at the grinding location is a back rest or a stationary support which prevents, in particular with an elongated workpiece, that this bends during the machining at the grinding location.
It has been found that the adjustment of such a workpiece carrier generally needs a lot of time and experience. In particular, in cases in which the workpieces are to be ground, the diameter of which are very small compared to their length, for example during the production of boring or milling workpieces with a diameter of only 1 mm or even smaller, the exact positioning of the workpiece carrier necessary for the accurate machining of the workpiece can require a long adjustment time in the region of the grinding location, during which one cannot work with the machine. While such long setting periods can be acceptable with workpieces to be produced in large quantities, they are particularly undesired if only a few workpieces are to be produced with the machine adapted once, before it is converted again.